Description: Alternate proof of equid and equid1 from older axioms ax-c7 , ax-c10 and ax-c9 . (Contributed by NM, 10-Jan-1993) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | equid1ALT | |- x = x |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-c9 | |- ( -. A. x x = x -> ( -. A. x x = x -> ( x = x -> A. x x = x ) ) ) |
|
| 2 | 1 | pm2.43i | |- ( -. A. x x = x -> ( x = x -> A. x x = x ) ) |
| 3 | 2 | alimi | |- ( A. x -. A. x x = x -> A. x ( x = x -> A. x x = x ) ) |
| 4 | ax-c10 | |- ( A. x ( x = x -> A. x x = x ) -> x = x ) |
|
| 5 | 3 4 | syl | |- ( A. x -. A. x x = x -> x = x ) |
| 6 | ax-c7 | |- ( -. A. x -. A. x x = x -> x = x ) |
|
| 7 | 5 6 | pm2.61i | |- x = x |